Abstract
This chapter is more mathematical. The theorems of Pappus, Desargues, and Pascal are introduced to show that there is a non-metrical geometry such as Poncelet had described. However, they are proved in a modern way, by reducing them to simple special cases and then using a mixture of elementary vector methods and theorems from elementary Euclidean geometry. The reductions use simple projective transformations, which leads to discussion of the idea of augmenting the familiar plane with a line at infinity. The concept of the cross-ratio of four points on a line is introduced and shown to be invariant under a projective transformation. Poncelet’s porism is described.
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© 2011 Springer-Verlag London Limited
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Gray, J. (2011). Theorems in Projective Geometry. In: Worlds Out of Nothing. Springer Undergraduate Mathematics Series. Springer, London. https://doi.org/10.1007/978-0-85729-060-1_3
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DOI: https://doi.org/10.1007/978-0-85729-060-1_3
Publisher Name: Springer, London
Print ISBN: 978-0-85729-059-5
Online ISBN: 978-0-85729-060-1
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